Year 12
Mathematics Extension 2 Syllabus 

Algebra of complex numbers: Cartesian, polar, and exponential forms

De Moivre’s Theorem and applications

Complex roots of polynomials

Advanced proof techniques including induction and contradiction

Kinematics: motion in a straight line and in a plane

Newton’s laws and applications

Circular motion and projectile motion

Work, energy, and momentum

Vector operations in two and three dimensions

Scalar and vector products

Applications to geometry and mechanics

Equations of lines and planes

Constructing and interpreting mathematical models

Applying calculus and vectors to real-world problems

Problem-solving with a focus on reasoning and justification

Further differentiation techniques (e.g. logarithmic, parametric, implicit)

Integration by parts and substitution

Applications to area, volume, and motion

Differential equations: solving and interpreting